1. FRACTIONS, DECIMALS AND PERCENTAGES
They’re all just different ways of saying the same thing

2. “FRACTION” means “part of”
Fraction is short for “vulgar fraction” or “common fraction” — e.g. 2/5
Decimal is short for “decimal fraction” —e.g. 0.4
Percentage means “out of one hundred” so it’s just a fraction with the bottom number % means 40/100

3. In each diagram, the same area is shaded
2/ %
But it’s not easy to see that the Fraction, the Decimal and the Percentage all have the same value, because the Fraction and the Decimal have been simplified

4. This time, the Fraction and the Decimal have both been left as “hundredths”
40/ %
Can you see the relationship, now that the Fraction and the Decimal have not been simplified?

5. Here are some common fractions which have not been simplified:
Decimal
Percentage
5/100
0.05 5%
10/100
0.10
10%
20/100
0.20
20%
25/100
0.25
25%
50/100
0.50
50%
75/100
0.75
75%
99/100
0.99
99%

6. The equivalence between Fractions, Decimals and Percentages is easy to spot, if you:
Write all fractions with the bottom number 100 — the top number is your percentage
Write all decimals with 2 decimal places — those 2 decimal places show your percentage
But now we have to look at how fractions and decimals get simplified . . .